Structural Balance and Signed International Relations

By Doreian, Patrick; Mrvar, Andrej | Journal of Social Structure, January 1, 2015 | Go to article overview

Structural Balance and Signed International Relations


Doreian, Patrick, Mrvar, Andrej, Journal of Social Structure


1. Introduction

A considerable effort (see below) has gone into the study of international relations between nations as sovereign entities.1 This work has included the use of structural balance theory for signed social relations in the version based on the work of Heider (1946) and its formalization by Cartwright and Harary (1956). Within the structural balance approach there are several prominent concerns. Given a definition of a balanced network (defined below), one is whether an empirical signed network is balanced or not. A second concern, for imbalanced networks, is to measure the extent to which they depart from being balanced. A third concern is to understand the dynamics of movement towards (or away from) balance with the presumption that signed networks move towards a balanced state.2 Using balance theory to study international relations was a natural application. Here, we consider these three concerns but use temporal global signed networks rather than partial networks for local regions for a particular point in time. This permits a more extensive study of the dynamics of structural balance and sheds considerable light on the dynamics of international signed relations.

Our primary objective was to apply structural balance theory to the signed networks of states from 1946 through 1999 in order to study the evolution of this network as it expanded in size to 64 states to a high of 155 states. In addition to changing size of the network, ties were created, dropped or changed in sign for states already in the network. Section 2 provides an outline of the key balance theoretic ideas informing this study. In Section 3, a variety of broad general theoretical approaches to studying the system of nations are presented. While these theories are seen as rivals to each other, we did not intend to enter the many debates about how nations behave and how the overall system operates. Nor did we see balance theoretic ideas as necessarily antithetical to those endeavors. However, given our results, we were drawn into these substantive debates. Section 4 contains a description of the data we used and the methods we employed. Signed blockmodeling results are reported in Section 5. They reveal the overall structure of the evolving network as it expanded. Section 6 presents measures of imbalance through time along with discussion of them. Overall summaries of our results are given in Section 7. A discussion of their implications for future work concludes our presentation in Section 8.

2. Balance Theoretic Ideas

Although there have been a variety of approaches to studying signed relations among human actors, Heider (1946, 1958) is credited with the first systematic statement of consistency theories (Taylor, 1970). His early statement provided the foundation for the Cartwright and Harary (1956) and Davis (1967) formalizations creating the two structure theorems that became the foundation for a fruitful approach for studying signed networks (Doreian and Mrvar, 1996). They drive the blockmodeling approach for partitioning signed relations described in Section 4.2. Of critical concern in the early work was the extent to which signed structures were balanced or consistent with regard to the pattern of signs. Ways of doing this are described in Section 2.2. The results of some earlier empirical work based on balance theoretic ideas is described in Section 2.3.

2.1 Foundations

The core ideas of Heider (1946) are located in triples of actors, denoted by p, o, and q, as shown in Figure 1. A triple consists of the ties p ^ o, o ^ q and p ^ q. These are the eight possible poq-triples where solid lines represent positive ties and dashed lines represent negative ties. The sign of a poq-triple is the product of the signs in the triple. A poq-triple is balanced if its sign is positive and imbalanced if its sign is negative. A complete signed network is balanced if all its triples are balanced. Figure 1 shows the four possible balanced triples in the top row and the four possible imbalanced triples in the bottom row. …

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